图 书 馆
非参数可信集的置信度？Confidence in nonparametric credible sets? |
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| 课程网址: | http://videolectures.net/isba2012_van_der_vaart_confidence/ |
| 主讲教师: | Aad van der Vaart |
| 开课单位: | 阿姆斯特丹大学 |
| 开课时间: | 2012-08-22 |
| 课程语种: | 英语 |
| 中文简介: |  在非参数统计中，后验分布的使用方式与任何贝叶斯分析中的使用方式完全相同。据推测，它为我们提供了给定数据的各种参数值的可能性。与参数分析的不同之处在于，通常很难对先验有直观的理解，这会影响作为不确定性量化的后验分布的可信度。第二个区别是后验分布对先验更敏感：它的“优良特性”很重要。即使在数据的信息量无限增加的渐近情况下也是如此。在本次演讲中，我们首先回顾了过去十年中获得的关于半和非参数设置中的后验分布的频率论渐近结果和见解。这些结果表明，如果在选择先验时要小心，后验分布可以有效地恢复真实参数。我们接下来继续询问后验分布是否也能够给出重建中的错误的正确概念。可信集是否与置信区域有任何可比性？我们不会给出这个问题的答案，而是通过例子表明它会很微妙。 |
| 课程简介: | In nonparametric statistics the posterior distribution is used in exactly the same way as in any Bayesian analysis. It supposedly gives us the likelihood of various parameter values given the data. A difference with parametric analysis is that it is often difficult to have an intuitive understanding of the prior, which affects the believability of the posterior distribution as a quantification of uncertainty. A second difference is that the posterior distribution is much more sensitive to the prior: its “fine properties” matter. This is true even in the asymptotic situation when the informativeness of the data increases indefinitely. In this talk we start by reviewing frequentist asymptotic results and insights on posterior distributions in the semi- and nonparametric setting obtained in the last decade. These results show that posterior distributions can be effective in recovering a true parameter provided some care is taken when choosing a prior. We next go on to ask whether posterior distributions are also capable in giving a correct idea of error in the reconstructions. Are credible sets in any way comparable to confidence regions? We shall not present an answer to this question, but show by example that it will be delicate. |
| 关 键 词: | 参数分析; 可信集; 不确定性量化 |
| 课程来源: | 视频讲座网 |
| 数据采集: | 2021-07-07：liyy |
| 最后编审: | 2021-07-09：liyy |
| 阅读次数: | 57 |